How did you manage to separate the screen off and have it stay in connected standby. Usually it is Screen off = Sleep
In the old days, you could tell PC - turn of screen after X minutes, NEVER sleep.
I cannot find a way to do this in the SP3.
There is no separation. when the screen is off it is in sleep (unless you actually shut it down). While in sleep, it is connected standby for the first 4 hours while on battery or permanent connected connected standby if plugged in.